Table 1 Results from GLMMs analyzing latitudinal and elevational patterns in seed predation.

Models are described in the text. Model 4 (effect of biome) and model 5 (forests only) were run twice, first on total predation (uncaged depots only) and then on invertebrate predation (caged depots only). Initial models (gray rows) included all possible interactions (indicated by “×”), but nonsignificant interactions were dropped from final models (white rows), improving model convergence. Significance of factors and interactions was obtained from testing the final model against a model without that factor or interaction. Effect sizes are given for noninteracting effects in the final model; for categorical variables, these are categorical latitude = temperate versus tropical, seed type = sunflower versus oat, cage treatment = uncaged (total predation) versus caged (invertebrate predation), and biome = below trees versus above trees (top) and within forest versus above trees (bottom).

Model
no.—predation
type, biomes
Fixed effectsχ2(df) statistic from likelihood ratio tests
Effect size ±SE in the final model (logit scale)
Model χ2
deviance
(residual df)
R2GLMM
Latitude
(decimal
degrees)
Elevation
(km asl)
Seed
species,
df = 1
Lat × Elev,
df = 1
Additional factor
1—Total, AllInitial:
categorLat ×
elev × seed.
sp
Final: categorLat
+ elev + seed.
sp
20.6(1)***
−0.48 ± 0.10
8.0(1)**
−0.18 ± 0.06
50.5***
0.46 ± 0.07
1.6, P > 0.11500(464)0.053
2—Total, AllInitial: lat × elev
× seed.sp
Final: lat + elev
+ seed.sp
17.5(1)***
−0.01 ± 0.003
7.0(1)**
−0.17 ± 0.06
55.2***
0.48 ± 0.07
2.6, P > 0.11501(464)0.058
3—Tot vs. Invert,
All
Initial: lat × elev
× cage.treat
Cage treat:
Final: lat × elev
+ cage.treat
39.0(2)***
21.8(2)***
7.5 **
−0.01 ± 0.004
13.7(1)***
0.32 ± 0.09
704(195)0.083
4t—Total, AllInitial: lat × elev
× seed.sp. ×
biome
Biome:
Final: lat + elev
+ seed.sp. +
biome
6.4(1)*
−0.007 ± 0.003
2.6(1) P > 0.1
−0.11 ± 0.07
54.7***
0.48 ± 0.07
2.6, P > 0.18.0(2)*
0.20 ± 0.23
0.44 ± 0.23
1493(462)0.057
4i—Invert, AllInitial: lat × elev
× biome
Biome:
Final: lat + elev
+ biome
10.0(1)**
−0.02 ± 0.005
6.3(1)*
−0.31 ± 0.13
2.2, P > 0.18.1(2)*
0.78 ± 0.39
0.84 ± 0.30
350(94)0.123
5 t—Total, ForestInitial: lat × elev
× seed.sp
Final: lat × elev + seed.sp8.6(2)*
8.0(2)*
45.6***
−0.008 ± 0.004
4.3*
0.48 ± 0.07
1177(361)0.039
5i—Invert, ForestInitial: lat × elev
Final: lat + elev10.9(1)***
−0.02 ± 0.005
5.4(1)*
−0.28 ± 0.13
3.7, P = 0.06253(65)0.036

*P < 0.05.

**P < 0.01.

***P < 0.001.

†Pseudo conditional R2 (variance explained by both fixed and random effects) for GLMMs with link-specific theoretical variances, calculated via the r.squaredGLMM function in the R MuMIn package (49) according to (50).

‡Sunflower seeds only, including only sites and dates that included the vertebrate exclusion treatment.